In a previous paper, we developed tools which allowed us to confirm that several of the waves in Saturn’s rings were likely generated by resonances with fundamental sectoral normal modes inside Saturn itself. Here we use these same tools to examine eight additional waves that are probably generated by structures inside the planet. One of these waves appears to be generated by a resonance with a...

We describe a deterministic polynomial-time test that determining whether a nonzero ideal is a prime ideal in a Dedekind domain with finite rank. The techniques which we used are basis representation of finite rings and the Hermite and Smith normal forms.

Recently, Shestakov-Umirbaev solved Nagata’s conjecture on an automorphism of a polynomial ring. To solve the conjecture, they defined notions called reductions of types I–IV for automorphisms of a polynomial ring. An automorphism admitting a reduction of type I was first found by Shestakov-Umirbaev. Using a computer, van den Essen–Makar-Limanov–Willems gave a family of such automorphisms. In t...

We define the concept of a doset Hibi ring and a generalized doset Hibi ring which are subrings of a Hibi ring and are normal affine semigrouprings. We apply the theory of (generalized) doset Hibi rings to analyze the rings of absolute orthogonal invariants and special orthogonal invariants and show that these rings are normal and CohenMacaulay and has rational singularities if the characterist...

This paper describes the analysis of a novel isotropic suspension designed for use in a Micro Electro Mechanical System (MEMS) z-axis angular gyroscope. The suspension, consisting of six concentric interconnected rings rigidly attached to an anchored frame, supports a resonating proof mass whose line of oscillation precesses in the presence of rotation induced Coriolis force. The paper demonstr...

In this paper we consider a free associative algebra on three generators over an arbitrary field K. Given a term ordering on the commutative polynomial ring on three variables over K, we construct uncountably many liftings of this term ordering to a monomial ordering on the free associative algebra. These monomial orderings are total well orderings on the set of monomials, resulting in a set of...

finite field representation, optimal normal basis, palindromic representation A representation of the field GF(2n) for various values of n is described, where the field elements are palindromic polynomials, and the field operations are polynomial addition and multiplication in the ring of polynomials modulo x2n+1–1. This representation can be shown to be equivalent to a field representation of ...

A 6 month old patient is reported with a ring chromosome 18 confirmed by cytogenetic studies and in situ hybridisation. Her clinical features were similar to previous cases of ring chromosome 18 syndrome. The ring chromosome was inherited from the phenotypically and mentally normal mother with a mos 46,XX/47,XX, + r(18) karyotype.

For any normal commutative Hopf subalgebra K = k of a semisimple Hopf algebra we describe the ring inside kG obtained by the restriction of H-modules. If G = Zp this ring determines a fusion ring and we give a complete description for it. The case G = Zpn and some other applications are presented.

In the title compound, C20H14N2O, the phenyl ring is almost normal to the naphthalene ring system with a dihedral angle of 86.72 (9)°. The 4H-pyran ring fused with the naphthalene ring system has a boat conformation. In the crystal, mol-ecules are linked into a helical supra-molecular chain along the b axis via N-H⋯N hydrogen bonds. The chains are consolidated into a three-dimensional architect...